{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This notebook was prepared by [Donne Martin](https://github.com/donnemartin). Source and license info is on [GitHub](https://github.com/donnemartin/interactive-coding-challenges)."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Solution Notebook"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Problem: Given an array of (unix_timestamp, num_people, EventType.ENTER or EventType.EXIT), find the busiest period.\n",
    "\n",
    "* [Constraints](#Constraints)\n",
    "* [Test Cases](#Test-Cases)\n",
    "* [Algorithm](#Algorithm)\n",
    "* [Code](#Code)\n",
    "* [Unit Test](#Unit-Test)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Constraints\n",
    "\n",
    "* Can we assume the input array is valid?\n",
    "    * Check for None\n",
    "* Can we assume the elements of the input array are valid?\n",
    "    * Yes\n",
    "* Is the input sorted by time?\n",
    "    * No\n",
    "* Can you have enter and exit elements for the same timestamp?\n",
    "    * Yes you can, order of enter and exit is not guaranteed\n",
    "* Could we have multiple enter events (or multiple exit events) for the same timestamp?\n",
    "    * No\n",
    "* What is the format of the output?\n",
    "    * An array of timestamps [t1, t2]\n",
    "* Can we assume the starting number of people is zero?\n",
    "    * Yes\n",
    "* Can we assume the inputs are valid?\n",
    "    * No\n",
    "* Can we assume this fits memory?\n",
    "    * Yes"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Test Cases\n",
    "\n",
    "* None -> TypeError\n",
    "* [] -> None\n",
    "* General case\n",
    "\n",
    "<pre>\n",
    "timestamp  num_people  event_type\n",
    "3          2           EventType.EXIT\n",
    "1          2           EventType.ENTER\n",
    "3          1           EventType.ENTER\n",
    "7          3           EventType.ENTER\n",
    "9          2           EventType.EXIT\n",
    "8          2           EventType.EXIT\n",
    "\n",
    "result = Period(7, 8)\n",
    "</pre>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Algorithm\n",
    "\n",
    "Since the input is not sorted, we'll need to sort it first by timestamp, ascending.\n",
    "\n",
    "For each interval in the data set:\n",
    "\n",
    "* If this is an \"enter\" event, increment `curr_people`, else, decrement\n",
    "* Since we can have an \"enter\" and \"exit\" event for the same timestamp, we'll need to look ahead one\n",
    "    * If the next element has the same timestamp, hold off (continue) on updating `max_people` and `max_period`\n",
    "    * Watch out for indexing out-of-bounds at the end of the array\n",
    "* Update `max_people` and `max_period`\n",
    "\n",
    "Sorted:\n",
    "\n",
    "<pre>\n",
    "timestamp  num_people  event_type       curr_people  max_people       max_period\n",
    "1          2           EventType.ENTER  2            2                [1, 3]\n",
    "3          1           EventType.ENTER  3            2 (not updated)  [1, 3]\n",
    "3          2           EventType.EXIT   1            2                [3, 7]\n",
    "7          3           EventType.ENTER  4            4                [7, 8]\n",
    "8          2           EventType.EXIT   2            4                [7, 8]\n",
    "9          2           EventType.EXIT   0            4                [7, 8]\n",
    "</pre>\n",
    "\n",
    "Complexity:\n",
    "* Time: O(nlog(n)) for the sort\n",
    "* Space: O(1), assuming the sort is in-place"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Code"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "from enum import Enum\n",
    "\n",
    "\n",
    "class Data(object):\n",
    "\n",
    "    def __init__(self, timestamp, num_people, event_type):\n",
    "        self.timestamp = timestamp\n",
    "        self.num_people = num_people\n",
    "        self.event_type = event_type\n",
    "\n",
    "    def __lt__(self, other):\n",
    "        return self.timestamp < other.timestamp\n",
    "\n",
    "\n",
    "class Period(object):\n",
    "\n",
    "    def __init__(self, start, end):\n",
    "        self.start = start\n",
    "        self.end = end\n",
    "\n",
    "    def __eq__(self, other):\n",
    "        return self.start == other.start and self.end == other.end\n",
    "\n",
    "    def __repr__(self):\n",
    "        return str(self.start) + ', ' + str(self.end)\n",
    "\n",
    "\n",
    "class EventType(Enum):\n",
    "\n",
    "    ENTER = 0\n",
    "    EXIT = 1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "class Solution(object):\n",
    "\n",
    "    def find_busiest_period(self, data):\n",
    "        if data is None:\n",
    "            raise TypeError('data cannot be None')\n",
    "        if not data:\n",
    "            return None\n",
    "        data.sort()\n",
    "        max_period = Period(0, 0)\n",
    "        max_people = 0\n",
    "        curr_people = 0\n",
    "        for index, interval in enumerate(data):\n",
    "            if interval.event_type == EventType.ENTER:\n",
    "                curr_people += interval.num_people\n",
    "            elif interval.event_type == EventType.EXIT:\n",
    "                curr_people -= interval.num_people\n",
    "            else:\n",
    "                raise ValueError('Invalid event type')\n",
    "            if (index < len(data) - 1 and \n",
    "                    data[index].timestamp == data[index + 1].timestamp):\n",
    "                continue\n",
    "            if curr_people > max_people:\n",
    "                max_people = curr_people\n",
    "                max_period.start = data[index].timestamp\n",
    "                if index < len(data) - 1:\n",
    "                    max_period.end = data[index + 1].timestamp\n",
    "                else:\n",
    "                    max_period.end = data[index].timestamp\n",
    "        return max_period"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Unit Test"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Overwriting test_find_busiest_period.py\n"
     ]
    }
   ],
   "source": [
    "%%writefile test_find_busiest_period.py\n",
    "from nose.tools import assert_equal, assert_raises\n",
    "\n",
    "\n",
    "class TestSolution(object):\n",
    "\n",
    "    def test_find_busiest_period(self):\n",
    "        solution = Solution()\n",
    "        assert_raises(TypeError, solution.find_busiest_period, None)\n",
    "        assert_equal(solution.find_busiest_period([]), None)\n",
    "        data = [\n",
    "            Data(3, 2, EventType.EXIT),\n",
    "            Data(1, 2, EventType.ENTER),\n",
    "            Data(3, 1, EventType.ENTER),\n",
    "            Data(7, 3, EventType.ENTER),\n",
    "            Data(9, 2, EventType.EXIT),\n",
    "            Data(8, 2, EventType.EXIT),\n",
    "        ]\n",
    "        assert_equal(solution.find_busiest_period(data), Period(7, 8))\n",
    "        print('Success: test_find_busiest_period')\n",
    "\n",
    "\n",
    "def main():\n",
    "    test = TestSolution()\n",
    "    test.test_find_busiest_period()\n",
    "\n",
    "\n",
    "if __name__ == '__main__':\n",
    "    main()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Success: test_find_busiest_period\n"
     ]
    }
   ],
   "source": [
    "%run -i test_find_busiest_period.py"
   ]
  }
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